The satellite positioning system such as a global positioning system (GPS) or the like in which a receiver receives the positioning signal transmitted by an artificial satellite and the receiver can determine its position from the positioning signal is widely used for navigation support of a vehicle, an aircraft, a ship or the like. The receiver in this satellite positioning system calculates the distance with the artificial satellite from the positioning signal and calculates the receiver's position based on the calculated distance. The distance between the receiver and the artificial satellite that is calculated from this positioning signal is called a pseudo distance.
The satellite positioning system performs positioning calculation based on the pseudo distance between each artificial satellite and the receiver. Therefore, the precision of the calculation of this pseudo distance has a large influence on the precision of the positioning calculation. The pseudo distance includes an abnormal value generated by various causes, such as a clock error, an error based on the ionosphere, an error based on the troposphere, a noise, and the like. Therefore, it is important to remove this abnormal value appropriately for improving the precision of the positioning measurement in the satellite positioning system and improving stability when it is used.
For this reason, in the satellite positioning system, an abnormal value detection apparatus (called Integrity Monitor (IM)) which monitors a state in which the abnormal value occurs in time-series data such as the pseudo distance or the like measured sequentially is often used usually. In particular, in a system such as a ground based augmentation system (GBAS) in which the satellite positioning system is used for navigation of an aircraft, a high level of safety is required. Therefore, the abnormal value detection apparatus is indispensable for such system.
The abnormal value detection apparatus is disclosed in a document by Gang Xie titled “OPTIMAL ON-AIRPORT MONITORING OF THE INTEGRITY OF GPS-BASE LANDING SYSTEMS” Ph.D. Dissertation, Stanford University, pages 26-32, Mar. 2, 2004 (non-patent document 1). In the abnormal value detection apparatus for the satellite positioning system described in non-patent document 1, a model of a monitored phenomenon is modeled by using past data of the previous day and the days before that. In the abnormal value detection apparatus, a Gaussian distribution is assumed for each elevation angle width of 10 degrees as a model and each of the data is normalized by using a dispersion value obtained for each elevation angle width of 10 degrees. The abnormal value detection apparatus assumes that the distribution of the normalized data follows the standard Gaussian distribution and detects a value which does not follow this standard Gaussian distribution as an abnormal value.
Further, an abnormal value detection apparatus for a satellite positioning system is disclosed in Japanese Patent Application Laid-Open No. 2009-68927 (patent document 1). The abnormal value detection apparatus for a satellite positioning system described in patent document 1 compares the worst value of the difference between values of a satellite orbit position in a predetermined effective period with a threshold value and determines the value of the satellite orbit position which is the origin of the worst value as the abnormal value when the worst value exceeds the threshold value.
However, there is a case in which the abnormal value detection apparatus described in non-patent document 1 and patent document 1 can not detect the abnormal value with high precision.
Namely, the abnormal value detection apparatus described in non-patent document 1 and patent document 1 assumes an invariant model based on the data in the past. Therefore, when an observation environment changes, there is a case in which the assumed invariant model cannot follow it. In such case, the calculation result cannot be trusted.
In addition, these abnormal value detection apparatuses do not take into account a time series correlation between data in the modeling. Therefore, when there is the time series correlation between data, these abnormal value detection apparatuses cannot detect this correlation. In this case, the calculation result includes an error.